Determinant of $\left[\begin{array}{cc}t & 3 t - 1\\1 & 3\end{array}\right]$

Calculate $\left|\begin{array}{cc}t & 3 t - 1\\1 & 3\end{array}\right|$.

The determinant of a 2x2 matrix is $\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$.

$\left|\begin{array}{cc}t & 3 t - 1\\1 & 3\end{array}\right| = \left(t\right)\cdot \left(3\right) - \left(3 t - 1\right)\cdot \left(1\right) = 1$

$\left|\begin{array}{cc}t & 3 t - 1\\1 & 3\end{array}\right| = 1$A